*3.5.3 Testing the stability of VAR models*

stationary at the first difference, the VAR model will be then combined with the error correction model becoming the vector error correction model (VECM). This study refers to the previous study, such as by Ascarya which mathematically

where *FDRt* is the financing-to-deposit ratio; *NPFt* is the nonperforming

The data analysis technique involves a technique that analyzes data and tests its validity [24]. This study uses parametric inferential statistical techniques, specifically the vector error correction model (VECM) method. It is used to determine the relationship either in the short- or in the long-term relationship among variables. In terms of the research design, the steps for data analysis technique are as follows:

The first step that must be done in the VECM estimation is to test stationary data. The data can be declared stationary if the time series data have a tendency to move toward the average. According to Kuncoro [25], those data are stationary when they are drawn against time. It will often pass through the horizontal axis, and autocorrelation will decrease regularly for a considerable lag. Subsequently, the data

b. Covariance between two data sequences depends on lags between the two

According to Basuki [26], to test the data stationarity, the augmented Dick-Fuller (ADF) test is used. If the t-ADF value is smaller than the MacKinnon critical value, it can be concluded that the data used are stationary or do not contain unit roots. The testing of the roots of this unit is carried out at the level up to the first difference. If the data level is not statistically achieved, a first difference test is

Time (lag) in economics is used to explain the dependence of one variable on another variable. The determination of lag length is done to determine the parameter estimates in VECM. In the VECM estimation, the causality relationship is strongly influenced by lag length. In addition, Basuki and Yuliadi [27] also

explained that if the lag entered is too short, it is feared that the resulted estimation is inaccurate. Conversely, if the lag entered is too long, it will produce inefficient

are considered as stationary if it meets the following two conditions:

a. The average covariance is constant over time.

*FDRt* ¼ Φ<sup>0</sup> þ Φ1*NPFt* þ Φ2*BOPOt* (4)

*NPFt* ¼ Φ<sup>0</sup> þ Φ1*BOPOt* þ Φ2*FDRt* (5)

*BOPOt* ¼ Φ<sup>0</sup> þ Φ1*FDRt* þ Φ2*NPFt* (6)

Risk on Islamic bank, which is formulated as follows:

financing; and *BOPOt* is the cost-to-income ratio.

**3.5 Research model and analysis method**

develops a general model as:

*Banking and Finance*

*3.5.1 Testing stationary data*

periods.

*3.5.2 Selecting lag length criteria*

necessary.

**56**

Before testing VAR estimation, a stability test must first be carried out. According to Basuki and Yuliadi [27], the stability of the model needs to be tested because it will affect the results of impulse response function (IRF) and variance decomposition (VDC). If stability is not tested, the results of the IRF and VDC analysis are invalid. A VAR system can be said to be stable or fulfill a stability test if the value of the entire root or root has a modulus smaller than one. In this study, it is known that the modulus value is less than one, which means that the result from IRF and VDC analyses is valid.

### *3.5.4 Testing cointegration test*

A cointegration test is the test intended to see whether there is a long-term relationship between a particular variable and another variable. In the VECM estimation, a cointegration test is very necessary to determine whether each variable has a relationship in the long-term or just short-term relationship. Technically, if the observed variables do not have a cointegration relationship, then the VECM estimation does not apply. If, the opposite, data had a relationship in the long term (cointegration), then VECM is applied.

According to Basuki and Yuliadi [27] as stated by Engle-Granger, the existence of non-stationary variables causes the possibility of a long-term relationship between variables in the system. The cointegration test is performed to determine the existence of the relationship between variables, especially in the long term. If there were cointegration on the variables used in the model, it can be ascertained that there is a long-term relationship between the variables. The *Johansen cointegration* method can be then used to test the existence of this cointegration.
